Precision Spectroscopy of Pionic $1s$ States of Sn Nuclei and Evidence for Partial Restoration of Chiral Symmetry in the Nuclear Medium

Deeply bound $1s$ states of ${\pi }^{-}$ in ${}^{115,119,123}\mathrm{S}\mathrm{n}$ were preferentially observed using the $\mathrm{S}\mathrm{n}(d,{}^3\mathrm{H}\mathrm{e})$ pion-transfer reaction under the recoil-free condition. The $1s$ binding energies and widths were precisely determined and were used to deduce the isovector parameter of the $s$-wave pion-nucleus potential to be $b_1=-(0.115\pm 0.007)m_{\pi }^{-1}$. The observed enhancement of $|b_1|$ over the free $\pi N$ value ($b_1^{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}/b_1=0.78\pm 0.05$) indicates a reduction of the chiral order parameter, $f_{\pi }^{*}(\rho {)}^2/f_{\pi }^2\approx 0.64$, at the normal nuclear density, $\rho ={\rho }_0$.

Figure 1

Double differential cross sections versus the ${}^3\mathrm{H}\mathrm{e}$ kinetic energy of the ${}^{124,120,116}\mathrm{S}\mathrm{n}(d,{}^3\mathrm{H}\mathrm{e})$ reactions measured at the incident deuteron energy of 503.388 MeV. The scales of the ${\pi }^{-}$ binding energies in ${}^{123,119,115}\mathrm{S}\mathrm{n}$ are also indicated.

Figure 2

Experimental values of $\{B_{1s},{\mathit{\Gamma }}_{1s}\}$ (elliptic circles for statistical errors, horizontal and vertical bars for total errors) for ${\pi }^{-}$ in ${}^{115,119,123}\mathrm{S}\mathrm{n}$, shown together with theoretical relations with $\{b_1,\mathrm{I}\mathrm{m}{B}_0\}$ for each isotope.

Figure 3

Likelihood contours in the $\{b_1,\mathrm{I}\mathrm{m}{B}_0\}$ plane from the simultaneous fitting of $\{B_{1s},{\mathit{\Gamma }}_{1s}\}$ of the $1s$ pionic states in the three Sn isotopes and three light symmetric nuclei. The previous ${}^{205}\mathrm{P}\mathrm{b}$ data reanalyzed with $\mathrm{I}\mathrm{m}{B}_0$ ($=0.046$) is shown for comparison.